Problem: $72$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $78$ less than $4$ times the number of away team fans. How many home team and away team fans attended the game?
Explanation: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 72}$ ${x = 4y-78}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${4y-78}$ for $x$ in the first equation. ${(4y-78)}{+ y = 72}$ Simplify and solve for $y$ $ 4y-78 + y = 72 $ $ 5y-78 = 72 $ $ 5y = 150 $ $ y = \dfrac{150}{5} $ ${y = 30}$ Now that you know ${y = 30}$ , plug it back into ${x = 4y-78}$ to find $x$ ${x = 4}{(30)}{ - 78}$ $x = 120 - 78$ ${x = 42}$ You can also plug ${y = 30}$ into ${x+y = 72}$ and get the same answer for $x$ ${x + }{(30)}{= 72}$ ${x = 42}$ There were $42$ home team fans and $30$ away team fans.